This book introduces the reader to the most important concepts and problems in the field of (2)-invariants. After some foundational
material on group von Neumann algebras, (2)-Betti numbers are defined and their use is illustrated by several examples. The
text continues with Atiyah's question on possible values of (2)-Betti numbers and the relation to Kaplansky's zero divisor
conjecture. The general definition of (2)-Betti numbers allows for applications in group theory. A whole chapter is dedicated
to Luck's approximation theorem and its generalizations. The final chapter deals with (2)-torsion, twisted variants and the
conjectures relating them to torsion growth in homology. The text provides a self-contained treatment that constructs the
required specialized concepts from scratch. It comes with numerous exercises and examples, so that both graduate students
and researchers will find it useful for self-study or as a basis for an advanced lecture course.